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About 2,103 papers for “hexagonal grid”

Hexagonal grid layer

Bollen, Martijn · Figshare · 2021

The hexagonal grid layer superimposed on the study area in Wallonia (Belgium). The resulting discretized space is used to allow inference on site-occupancy of wild boar. Consult Sections 2.2 and 2.3 of the manuscript for more information.

Cited by 0Open access

Hexagonal grid layer

Martijn Bollen · Figshare · 2021

The hexagonal grid layer superimposed on the study area in Wallonia (Belgium). The resulting discretized space is used to allow inference on site-occupancy of wild boar. Consult Sections 2.2 and 2.3 of the manuscript for more information.

Cited by 0Open access

ON THE HEXAGONAL GRID

Gunilla Borgefors · 1988

The hexagonal grid is a reasonable approximation of the human vision grid, is more suited to natural scenes than the square grid and avoids the 4neigbor/8-neighbor problem. Skeletons are good representations of digital shapes, and can be used for storage and shape editing. We compute efficient skeletons on the hexagonal distance transform. The computations can be performed either in parallel or sequentially, since only local operations are used.

Cited by 1

Worldwide Hexagonal Grid 7774km2

Adrián Martín-Taboada, Alisa Aliaga‐Samanez, Jesús Olivero et al. · Zenodo (CERN European Organization for Nuclear Research) · 2023

We made a worldwide hexagonal grid composed of 20,805 hexagonal 7774 km2 units, built using Discrete Global for R (https://github.com/r-barnes/dggridR).

Cited by 1Open access

Hexagonal Grid Polygons Online

Daniel Herrmann, Tom Kamphans, Elmar Langetepe · 2007

We investigate the online exploration problem (aka covering) of a short-sighted mobile robot moving in an unknown cellular environment with hexagons and triangles as types of cells. To explore a cell, the robot must enter it. Once inside, the robot knows which of the 3 or 6 adjacent cells exist and which are boundary edges. The robot’s task is to visit every cell in the given environment and to return to the start. Our interest is in a short exploration tour; that is, in keeping the number of multiple cell visits small. For arbitrary environments containing no obstacles we provide a strategy producing tours of length S ≤ C + 1 4E − 2.5 for hexagonal grids, and S ≤ C + E − 4 for triangular grids. C denotes the number of cells—the area—, E denotes the number of boundary edges—the perimeter—of the given environment. Further, we show that our strategy is 4 3-competitive in both types of grids, and we provide lower bounds of 14 7 13 for hexagonal grids and 6 for triangular grids. The strategies were implemented in a Java applet [20] that can be found in

Cited by 0

Worldwide Hexagonal Grid 2591km2

Martín-Taboada, Adrián, Aliaga-Samanez, Alisa, Olivero, Jesús et al. · Zenodo (CERN European Organization for Nuclear Research) · 2024

We made a worldwide hexagonal grid composed of 58612 hexagonal 2591 km2 units, built using Discrete Global for R (https://github.com/r-barnes/dggridR).

Cited by 0Open access

Hexagonal Grid and Wavelets in Image Processing: Study on Hexagonal grid and Hexagonal Wavelets in Image processing

Fayas Asharindavida · 2012

Image processing in hexagonal grid is very much advantageous than in the conventional rectangular grid. The advantages include higher angular resolution, consistent connectivity and higher sampling efficiency. A wide class of operations on images can be performed directly in the wavelet domain by operating on its coefficients of the images. Operating in wavelet domain enables to operate on different resolutions, manipulate features at different scales and localize the operation in both spatial and frequency domains. Many multiresolution image processing operations becomes faster and more efficient if it is done in wavelet domain. Hexagonal wavelet includes the advantages of the hexagonal grid along with the wavelets which will be very useful in multiresolution operations. A new method of designing hexagonal wavelets using lifting scheme in the spiral addressing scheme is proposed in this book. It is computationally efficient because they are not based on Fourier transforms, and could be performed in place.

Cited by 0

Hexagonal grid in Flanders, Belgium

Thierry Onkelinx, Raïsa Carmen, Thomas Scheppers · Open Natuur Archief (Open Nature Archive) · 2022

As part of the annual partridge spring counts in Flanders, hunters are required to count partridges in all areas that have suitable habitat for partridges (<em>Perdix perdix</em>). Since it is assumed that visibility is around 200 meters, this hexagonal grid with a distance of 400 meters between parallel sides, helps volunteers in choosing observation points.

Cited by 0Open access

Halftoning over a hexagonal grid

Pierre‐Marc Jodoin, Victor Ostromoukhov · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2003

In this contribution, we present an optimal halftoning algorithm that uniformly distributes pixels over a hexagonal grid. This method is based on a slightly modified error-diffusion approach presented at SIGGRAPH 2001. Our algorithm's parameters are optimized using a simplex downhill search method together with a <i>blue noise </i>based cost function . We thus present a mathematical basis needed to perform spectral and spatial calculations on a hexagonal grid. The proposed algorithm can be used in a wide variety of printing and visualization tasks. We introduce an application where our error-diffusion technique can be directly used to produce clustered screen cells.

Cited by 5

Distance on a Hexagonal Grid

Luczak, Rosenfeld · IEEE Transactions on Computers · 1976

A simple formula is derived for the distance between two points on a hexagonal grid, in terms of coordinates with respect to a pair of oblique axes.

Cited by 139

Hexagonal grid in Flanders, Belgium

Thierry Onkelinx, Raïsa Carmen, Thomas Scheppers · Zenodo (CERN European Organization for Nuclear Research) · 2022

As part of the annual partridge spring counts in Flanders, hunters are required to count partridges in all areas that have suitable habitat for partridges (<em>Perdix perdix</em>). Since it is assumed that visibility is around 200 meters, this hexagonal grid with a distance of 400 meters between parallel sides, helps volunteers in choosing observation points.

Cited by 0Open access

Visualization Using Hexagonal Grid IL-SOM

Inkyung Cho, Ju-Won Song · The Korean Data Analysis Society · 2019

자기조직화지도(SOM)는 고차원 다변량 자료를 저차원 그리드 공간에 축약하여 시각화하는 비지도 학습 신경망 모형의 일종이다(Kohonen, 1998). SOM은 개체를 각 승자노드의 중심에 할당하는데 개체의 연속성을 보존한다는 관점에서는 그리드 공간에 승자노드를 중심으로 개체들이 적절히 퍼지도록 분포시키는 게 바람직하다. Um(2003)은 개체벡터의 승자노드와 그 인접노드의 중량벡터에 대한 가능도를 이용하여 그리드 공간상에 개체벡터의 상대적인 위치를 표현하도록 SOM을 확장한 IL-SOM을 제안하였다. SOM에서는 사각형 또는 육각형 그리드를 주로 사용하는데 Um(2003)은 이차원 그리드 공간에 사각그리드와 가상노드를 통해 확장한 확장형 사각그리드를 구현하였고 개체표현지수(Um, 2003)가 최소화되는 그리드의 크기를 선택하면 개체를 가장 잘 시각화한다는 결론을 내렸다. 본 연구에서는 이차원 그리드 공간에 육각그리드와 가상노드를 통해 확장한 확장형 육각그리드를 사용하는 IL-SOM을 구현하였다. 모의실험을 통해 사각그리드, 확장형 사각그리드, 육각그리드와 확장형 육각그리드의 개체표현지수 및 자료의 시각화 결과를 비교하였다. 또한 이 방법들을 4개의 그룹으로 구성된 게 자료에 적용하여 개체표현지수를 최소화하는 그리드의 종류를 확인하고 이를 통해 자료를 시각화한 결과를 비교하였다. 사각그리드와 육각그리드 모두 가상노드가 없는 경우보다 있는 경우가 개체표현지수가 작아 더 좋은 결과를 보였으며 육각그리드가 사각그리드보다 대체로 나은 결과를 보였다.Self-organizing maps (SOM) is an unsupervised learning neural network model to visualize high dimensional data using a low dimensional grid space (Kohonen, 1990). SOM assigns objects to the center of the winning node, but it would be better to spread them all over the grid space to preserve continuity of the objects. Um (2003) proposed IL-SOM (interpolating using likelihood for SOM) to express relative locations of object vectors in a grid space using the likelihood of weight vectors of the winning node and its neighbor nodes. SOM usually uses the rectangular or the hexagonal grid. In a 2-dimensional rectangular grid, Um (2003) derived IL-SOM and extended it using a virtual nodes. In this study, IL-SOM is derived in a 2-dimensional hexagonal grid and extended using virtual nodes. A simulation is conducted to compare the performance of IL-SOM in the rectangular, the extended rectangular, the hexagonal and the extended hexagonal grid. These four methods are also compared with the crab data. In both rectangular and hexagonal grid, the extension using virtual nodes performed better. Performance of the hexagonal grid is usually better than the one of the rectangular grid.

Cited by 0

Hamilton Circuits in Hexagonal Grid Graphs

Kamrul Islam, et al. · 2007

We look at a variant of the Hamilton circuit problem, where the input is restricted to hexagonal grid graphs. A hexagonal grid graph has a vertex set that is a subset of the grid points of a regular hexagonal tiling of the plane and edges corresponding to hexagon sides. We show that Hamilton circuit in hexagonal grid graphs is NP-complete.

Cited by 0

Method of Building a Hexagonal Grid

Nickolay M. Zubashevskiy, Alexander Berkin · 2021 XV International Scientific-Technical Conference on Actual Problems Of Electronic Instrument Engineering (APEIE) · 2021

Let there is an image with some object made up of hexagons (for example, a photo of a microchannel plate). In this paper, the algorithm that builds a hexagonal grid on a photo of an object is considered. The main principle of the algorithm is detection the contour of the object. Then with the help of special geometric construction determine the coordinates of each nodal point of the hexagonal grid. The developed algorithm consists of several stages: the detection of the object edge, the corners detection on a two-dimensional curve, geometric constructions for determining the nodal points coordinates. At the same time, the widespread problem of edge detection in this case has a certain specificity. As a result of which a special algorithm for contour selection for this particular task was developed. The algorithm was also tested in conditions of high noise and uneven illumination of the object.

Cited by 1

Geometric transformations on the hexagonal grid

Innchyn Her · IEEE Transactions on Image Processing · 1995

The hexagonal grid has long been known to be superior to the more traditional rectangular grid system in many aspects in image processing and machine vision related fields. However, systematic developments of the mathematical backgrounds for the hexagonal grid are conspicuously lacking. The purpose of this paper is to study geometric transformations on the hexagonal grid. Formulations of the transformation matrices are carried out in a symmetrical hexagonal coordinate frame. A trio of new trigonometric functions are defined in this paper to facilitate the rotation transformations. A fast algorithm for rounding an arbitrary point to the nearest hexagonal grid point is also presented.

Cited by 160